{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#本章需导入的模块\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['font.sans-serif']=['SimHei']  #解决中文显示乱码问题\n",
    "plt.rcParams['axes.unicode_minus']=False\n",
    "import warnings\n",
    "warnings.filterwarnings(action = 'ignore')\n",
    "from scipy.stats import beta\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "import sklearn.linear_model as LM\n",
    "from sklearn.model_selection import cross_val_score,cross_validate,train_test_split\n",
    "from sklearn.metrics import classification_report\n",
    "from sklearn.metrics import roc_curve, auc,accuracy_score,precision_recall_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alphas= [1/3,2/3,1,2,4,10,20]\n",
    "betas = [1,2/3,1,6,4,30,20]\n",
    "colors =  ['blue', 'orange', 'green', 'red', 'purple', 'brown', 'black']\n",
    "theta = np.linspace(0, 1, 100)\n",
    "fig, ax = plt.subplots(figsize=(9,6))\n",
    "for a, b, c in zip(alphas, betas, colors):\n",
    "    dist = beta(a, b)\n",
    "    plt.plot(theta, dist.pdf(theta), c=c)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 6)\n",
    "plt.xlabel(\"theta\")\n",
    "plt.ylabel(r'$p(theta|\\alpha,\\beta)$')\n",
    "plt.title('Beta分布')\n",
    "ax.annotate('Beta(1/3,1)', xy=(0.014, 5), xytext=(0.04, 5.2),arrowprops=dict(facecolor='black', arrowstyle='-'))\n",
    "ax.annotate('Beta(10,30)', xy=(0.276, 5), xytext=(0.3, 5.4),arrowprops=dict(facecolor='black', arrowstyle='-'))\n",
    "ax.annotate('Beta(20,20)', xy=(0.5, 5), xytext=(0.52, 5.4),arrowprops=dict(facecolor='black', arrowstyle='-'))\n",
    "ax.annotate('Beta(2,6)', xy=(0.256, 2.41), xytext=(0.2, 3.1),arrowprops=dict(facecolor='black', arrowstyle='-'))\n",
    "ax.annotate('Beta(4,4)', xy=(0.53, 2.15), xytext=(0.45, 2.6),arrowprops=dict(facecolor='black', arrowstyle='-'))\n",
    "ax.annotate('Beta(1,1)', xy=(0.8, 1), xytext=(0.7, 2),arrowprops=dict(facecolor='black', arrowstyle='-'))\n",
    "ax.annotate('Beta(2/3,2/3)', xy=(0.99, 2.4), xytext=(0.86, 2.8),arrowprops=dict(facecolor='black', arrowstyle='-'))\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
